Before giving the details of the computation of (REF ), we note that applying the convergence result of [1]}, and denoting \(D_{\mathcal {P}} = \max \limits _{P, P^{\prime } \in \mathcal {P}}\Vert P- P^{\prime }\Vert \)  the diameter of \(\mathcal {P}\) , we obtainIn more details, the convergence guarantee of [1]} uses the operator norm of \({u}\)  and \({v}\) , which we bound as follows: \({u(P)}^2 \le \sum _{i} \sum _{j,k} (\mu _{ij}P_{ijk} {b}_k)^2 \le {b}_1^2 {P}^2\) , because \(\mu _{ij}\in [0,1]\)  \({b}_k \in [0,{b}_1],\)  and similarly \({{v}(P)}^2 \le {b}_1^2 {P}^2\) .:
